Integration theory for kinks and sphalerons in one dimension
N. S. Manton
Abstract
Abstract The static kink, sphaleron and kink chain solutions for a single scalar field φ in one spatial dimension are reconsidered. By integration of the Euler–Lagrange equation, or through the Bogomolny argument, one finds that each of these solutions obeys a first-order field equation, an autonomous ODE that can always be formally integrated. We distinguish the BPS case, where the required integral is along a contour in the φ -plane, from the semi-BPS case, where the integral is along a contour in the Riemann surface double-covering the φ -plane, and is generally more complicated.
Topics & Concepts
Scalar fieldOdeMathematicsMethods of contour integrationRiemann hypothesisScalar (mathematics)Dimension (graph theory)Mathematical analysisPlane (geometry)Euler's formulaSphaleronMathematical physicsGeometryPure mathematicsPhysicsQuantum mechanicsHiggs bosonBaryogenesisOrbital Angular Momentum in OpticsAdvanced Fiber Optic SensorsAdvanced Fiber Laser Technologies